Expressive Tuning and Equal Temperament

There is a school of thought that sees equal temperament as a Bad Thing. It is presented as a kind of industrialisation of a natural process, imposing a new regulative order on the west’s approach to music, commodifying our ways of hearing at the same time as mass-production processes were applied to pianos and popular songs.

Equal temperament was not adopted because it sounded better (it didn't then, and it still doesn't, despite 150 years of cultural conditioning) or because composers and theorists were unaware of Just Intonation. The adoption of twelve-tone equal temperament was strictly a matter of expediency. Equal temperament allowed eighteenth- and nineteenth-century composers to explore increasingly complex harmonies and abstruse modulations, but this benefit was short-lived. By the beginning of this century, all of the meaningful harmonic combinations in the equally-tempered scale had been thoroughly explored and exploited, and many composers believed that consonance, tonality, and even pitch had been exhausted as organizing principles. What was really exhausted was merely the limited resources of the tempered scale. By substituting 12 equally-spaced tones for a universe of subtle intervallic relationships, the composers and theorists of the 18th and 19th centuries effectively painted western music into a corner from which it has not yet succeeded in extricating itself.

I rather like this version of the narrative, since it inflects the standard story of paradise lost with the experience of the rake whose quest for ever more extreme sexual experiences exhausts his capacity for any kind of authentic feeling.

And there’s something to this story, of course. Period instrument bands who play with justly-tuned thirds and fifths give us a glow, a richness in the sound quite different from the brightness produced by modern instrument manufacture. And those of us involved in a cappella vocal genres know the visceral and sonic pleasures to be had from the experience of ‘lock and ring’.

But I heard an interesting counter-argument to this position at the weekend, at Birmingham Conservatoire’s annual research study day. Our Head of Research, Peter Johnson, who is something of a pioneer in the empirical study of performance, presented a paper about how violinists tune when they’re playing along with pianos tuned in equal temperament. (The answer: sharp, if they’re Menuhin.)

In the course of this he made one of those throw-away remarks that is so interesting you miss the next five minutes of the main argument while you think about it. He was talking about Casals’ theory of expressive intonation: that you should sharpen rising semitones (as they are functional leading notes) and flatten falling ones (as functional 7ths). Peter has shown in previous work that Casals does indeed play like this, and that such tuning habits relate to longer-range voice-leading as well as immediate note-to-note examples. The throw-away remark was that equal temperament does this too, though to a smaller degree than Casals did on the cello.

So, let’s think about that for a moment. The major 3rd in just intonation is defined by the ratio of 5:4, and comes out in cents as 386.314, whereas the equally-tempered major 3rd is 400 cents – i.e. slightly sharper. The minor seventh is less simple, since it could be defined in one of three ways in just intonation: the harmonic minor 7th (7:4, 968.826 cents), the grave minor 7th (16:9, 996.091 cents) or the adjective-less minor 7th (9:5, 1017.597 cents). Of these, only the last is actually greater than the equally tempered minor 7th of 1000 cents, but still, that still leaves room to claim that equal temperament raises 3rds and flattens 7ths compared to just intonation.

The point this makes of course is that it reframes equal temperament as not merely a chromatically expedient system, but as an expressively coherent one. Yes, it still places it in the service of the harmonic adventures of functional tonality, but the service it’s performing is to amplify the sense of direction and teleology built by tonal structures. Equal temperament stops looking like a cheap imitation tuning system that can be sold to oiks who are too unskilled to retune their own keyboards between pieces in different keys, and starts looking more like a harmonic flavour enhancer: a kind of musical monosodium glutamate. Not the most heroic revisionist metaphor, I know, but musically useful nonetheless.